(Solved): Find the general soiution of the given differential equation. \[ \cos ^{2}(x) \sin (x) \frac{d y}{d ...

Find the general soiution of the given differential equation. \[ \cos ^{2}(x) \sin (x) \frac{d y}{d x}+\left(\cos ^{3}(x)\right) y=1 \] \( y(x)= \) Give the largest interval 1 over which the general solution is defined. (Think abolt the implications of any singular points.) \( (-1,1) \) \( \left(0, \frac{\pi}{2}\right) \) \( \left(-\frac{\pi}{2}+\frac{\pi}{2}\right) \) \( (0, x) \) \( \left(-x^{2}, \infty\right) \) Determine whether there are any transient terms in the general solution, (Enter the transient terms as a comma-separafed ilst; if there are none, enter NoNE)